Digital Signal Processing Using Matlab

2.3. Exercises

EXERCISE 2.15.

Calculate and plot the spectrum of a periodic rectangular pulse of period N = 16, if:

Note the values of spectral components c₀ and c_N/2, and show that c_{N – k} = c*_k for k = 0.15.

EXERCISE 2.16.

Verify the linearity property of the DTFT_1D:

using the following signals:

with a₁ = 1 and a₂ = 0.5.

EXERCISE 2.17.

Generate and plot the following signals:

Verify that the imaginary part of the DTFT of signal x₁ [n] is zero; do the same for the real part of the DTFT of signal x₂[n].

EXERCISE 2.18.

Show that the DTFT_1D is the same for the two discrete-time signals defined below:

EXERCISE 2.19.

Write a MATLAB code to verify Parseval's theorem:

for the signal:

EXERCISE 2.20.

Write a MATLAB code to verify that the following exponential signal family:

a) contains only ...